Topological Flexural Modes in Polarized Bilayer Lattices

TL;DR

This paper demonstrates that topological properties in bilayer kagome lattices can be transferred to control out-of-plane flexural waves, enabling new ways to manipulate mechanical vibrations in thin sheets.

Contribution

It introduces a bilayer lattice design that couples in-plane topological modes to out-of-plane flexural responses, expanding topological mechanics into the realm of flexural wave control.

Findings

Existence of out-of-plane topological modes in bilayer kagome lattices

Laser vibrometer experiments confirm simulation predictions

Potential for designing flexural wave devices with polarized responses

Abstract

Topological lattices have recently generated a great deal of interest based on the unique mechanical properties rooted in their topological polarization, including the ability to support localized modes at certain floppy edges. The study of these systems has been predominantly restricted to the realm of in-plane mechanics, to which many topological effects are germane. In this study, we stretch this paradigm by exploring the possibility to export certain topological attributes to the flexural wave behavior of thin lattice sheets. To couple the topological modes to the out-of-plane response, we assemble a bilayer lattice by stacking a thick topological kagome layer onto a thin twisted kagome lattice. The band diagram reveals the existence of modes whose out-of-plane character is controlled by the edge modes of the topological layer, a behavior elucidated via simulations and confirmed via laser vibrometer experiments on a bilayer prototype specimen. These results open an alternative direction for topological mechanics whereby flexural waves are controlled by the in-plane topology, leading to potential applications for flexural wave devices with engineered polarized response.